Unsupervised Relation Extraction (RE) aims to identify relations between entities in text, without having access to labeled data during training. This setting is particularly relevant for domain specific RE where no annotated dataset is available and for open-domain RE where the types of relations are a priori unknown. Although recent approaches achieve promising results, they heavily depend on hyperparameters whose tuning would most often require labeled data. To mitigate the reliance on hyperparameters, we propose PromptORE, a "Prompt-based Open Relation Extraction" model. We adapt the novel prompt-tuning paradigm to work in an unsupervised setting, and use it to embed sentences expressing a relation. We then cluster these embeddings to discover candidate relations, and we experiment different strategies to automatically estimate an adequate number of clusters. To the best of our knowledge, PromptORE is the first unsupervised RE model that does not need hyperparameter tuning. Results on three general and specific domain datasets show that PromptORE consistently outperforms state-of-the-art models with a relative gain of more than 40% in B 3 , V-measure and ARI. Qualitative analysis also indicates PromptORE's ability to identify semantically coherent clusters that are very close to true relations.